Doppler-shifted cyclotron resonance with helicons in aluminum

Doppler-shifted cyclotron resonance (DSCR) has been observed with helicon waves propagating along the [001], [110], and [111] axes of pure aluminum crystals. Strong quantum oscillations are observed in all propagation directions, the periods of the quantum oscillations agreeing with those of the long-period de Haas-van Alphen oscillations. The dispersion relations of the helicons as well as the frequencies and field values of the DSCR surface impedance anomalies have been measured and compared to the values calculated from two current models for the aluminum Fermi surface. The nonlocal dispersion forB [001] follows closely the theoretical results, while the nonlocal effect forB [110] is weaker than expected. A helicon window and a negative nonlocal dispersion are observed forB [111], due to the resonance of the electron states on the second-zone cap region. Except for those appearing below the helicon window, all the field-frequency relations of the experimental DSCR anomalies agree with those calculated from the predicted resonance zones at the Fermi surface.Work supported by the National Science Foundation.     

Acousto-optic cell based on paratellurite crystal with surface excitation of acoustic waves

An acousto-optic cell based on a paratellurite (TeO₂) crystal, in which bulk acoustic waves are excited directly from the surface due to an intrinsic piezoelectric effect in the material, has been studied. The bulk shear acoustic waves with a frequency of 50 MHz propagate along the [001] and [110] axes with a polarization along the [ [`1]10 ]\left[ {\bar 110} \right] axis. The ultrasound has been excited by a simple system of two electrodes formed on one face of the crystal. Characteristics of the acousto-optic cell have been determined and the parameters of acoustic waves have been measured at 633 nm by optical beam diffraction on the acoustic diffraction grating.     

On nonlocal microfluid mechanics

The simple microfluid theory of Eringen [1] is generalized to include nonlocal effects. The balance laws, jump conditions, and constitutive equations are obtained. The nonlocal intermolecular forces, energy and entropy are accounted for by nonlocal field residuals and functional constitutive equations of space type. The second law of thermodynamics is used to obtain specific forms of these residuals, constitutive equations and restrictions to be imposed. The linear theory is developed fully for the micromorphic and micropolar nonlocal fluids. The nonlocal effects are shown to include surface tension and surface stresses. Passage is made to material gradient theories.     

Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates

In this paper, a three dimensional vibration analysis of nano-plates is studied by decoupling the field equations of Eringen theory. Considering the small scale effect, the three dimensional equations of nonlocal elasticity are obtained. At first, three decoupled equations in terms of displacement components and three decoupled equations in terms of rotation components are obtained. In order to find the solution for a nano-plate based on the presented formulation, one of the three equations in terms of displacement components and corresponding rotation equation should be solved independently. Using some relations, the other two displacement components can be obtained in terms of the mentioned displacement and rotation component. A Navier-type method for finding the exact three dimensional solution of a nano-plate is presented using the Fourier series technique. Exact natural frequencies of nano-plates are presented and compared with the results of nonlocal first order and third order shear deformation theories.     

On the nonlocal aspects of the propagation of Love waves

Propagation of Love waves in an isotropic homogeneous elastic medium is analyzed in the context of the linear theory of nonlocal continuum mechanics. The dispersion equation, obtained for the plane transverse horizontally polarized waves in an infinite space, is compared with the corresponding equation given by the atomic lattice dynamics in order to determine a nonlocal modulus. It is found that the lower bound for the speed of Love waves predicted by the nonlocal theory agrees better with the seismological observations of such waves than its counterpart furnished by the conventional theory.     

Longitudinal waves in a nonlocal rod by fractional Laplacian

ABSTRACT

The article deals with the longitudinal waves in a nonlocal elastic rod. Regarding the nonlocal elasticity the Eringeen model has been assumed; the novelty is that this model is described in terms of the fractional Laplace operator. The standing waves are obtained by numerical solutions of the fractional differential equation in one-dimensional continuum. The obtained results are in accordance with the ones reported in the literature and highlight the dispersion phenomenon. The effects of the nonlocal contribution and of the fractional Laplacian order are also analyzed.     

The propagation of plane waves in bilevel anisotropic elastic solids with nonlocal polar constitution

In analyzing problems involving material behavior from the standpoint of generalized continuum mechanics, one is often faced with different forms of anisotropy at different levels of microscopic and macroscopic aggregates within the same material. In this article, a continuum theory incorporating nonlocal effects within the microstructure of anisotropic solids is developed. In order to illustrate the mathematical development of the theory in practical applications, the theory is applied to the case of materials possessing orthotropy on the nonlocal micropolar level and transverse isotropy on the local micropolar level. This case may apply to materials such as wood and wood composites. The resulting field equations are solved for the propagation of plane waves in a bilevel, anisotropic, nonlocal, micropolar elastic solid.     

An experimental verification of nonlocal fracture criterion

By using a nonlocal field theory, Eringer et al. [6] obtained a finite solution for the stress at the tip of a sharp crack. This solution permitted the development of a nonlocal fracture criterion for crystalline materials that is given in terms of atomic distance and theoretical cohesive strength.

The nonlocal fracture criterion is generalized for application to real materials by the introduction of a characteristic dimension (a measure of the size of the internal structures). Particleboard, a wood-based composite with controllable internal characteristics (particle dimensions and amount of resin), is used to substantiate the nonlocal fracture criterion.     

Boundary effect on weight function in nonlocal damage model

Some insights on boundary effects in nonlocal damage modelling are addressed. Interaction stresses that are at the origin of nonlocality are expected to vanish at the boundary of a solid, in the normal direction to this boundary. Existing models do not account for such an effect. We introduce tentative modifications of the classical nonlocal damage model aimed at accounting for this boundary layer effect in a continuum modelling setting. Computations show that some nonnegligible differences may be observed between the classical and modified formulations. In a one dimensional spalling test, only the modified formulation provides a spall of finite nonzero thickness, whereas spalls smaller than the internal length cannot be obtained according to the original formulation. For the same set of model parameters, including the internal length, the fracture energy derived from the size effect test method is also very different according to both approaches. Parameters in the size effect laws for notched and unnotched specimens, obtained from computation of geometrically similar bending beams, are more consistent with the modified nonlocal model compared to the original nonlocal formulation.     

Multiple surface plasmon waves in [prism/Ag/SiO2 helical thin film] Kretschmann configuration

Two surface plasmon resonance dips in reflectance angular spectrum for a p-polarized incident beam of a [prism/Ag/SiO₂ helical thin film] Kretschmann configuration are measured and compared with simulations. The simulation also shows that the angular positions of resonances due to surface plasmon waves in reflectance spectrum are sensitive to the variation of principal refractive indices of helical films. It indicates that multiple surface plasmon waves at the [Ag/SiO₂ helical thin film] interface is more attractive than the traditional method of producing only one surface plasmon wave for chemical- and bio-sensing applications.     

A method for multidimensional wave propagation analysis via component‐wise partition of longitudinal and shear waves

An explicit integration algorithm for computations of discontinuous wave propagation in two‐dimensional and three‐dimensional solids is presented, which is designed to trace extensional and shear waves in accordance with their respective propagation speeds. This has been possible by an orthogonal decomposition of the total displacement into extensional and shear components, leading to two decoupled equations: one for the extensional waves and the other for shear waves. The two decoupled wave equations are integrated with their CFL time step sizes and then reconciled to a common step size by employing a previously developed front‐shock oscillation algorithm that is proven to be effective in mitigating spurious oscillations. Numerical experiments have demonstrated that the proposed algorithm for two‐dimensional and three‐dimensional wave propagation problems traces the stress wave fronts with high‐fidelity compared with existing conventional algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Propagation of Rayleigh surface waves with small wavelengths in nonlocal visco-elastic solids

This paper investigates Rayleigh waves, propagating on the surface of a visco-elastic solid under the linear theory of nonlocal elasticity. Dispersion relations are obtained. It is observed that the waves are dispersive in nature for small wavelengths. Numerical calculations and discussions presented in this paper lead us to some important conclusions.     

Continuum model of two-dimensional crystal lattice of metamaterials

The continuum models of two-dimensional crystal lattice of metamaterial are investigated in this paper. The equivalent classical continuum requires the introduction of frequency-dependent mass density that becomes negative or infinite near the resonance frequency. In order to avoid the frequency-dependent mass density and make the dispersive characteristic of the elastic waves propagating in the equivalent continuum approximating that of lattice wave in two-dimensional crystal lattice of metamaterial, three kinds of continuum models, namely, the multiple displacements continuum model, the strain gradient continuum model and the nonlocal strain gradient continuum model, are investigated. It is found that the nonlocal gradient continuum model may better represent the dispersive relation and the bandgap characteristics of the metamaterial by the appropriate selection of nonlocal parameters.     

Effect of competing cubic-quintic nonlinearities on the modulational instability in nonlocal Kerr-type media

We investigate analytically and numerically the modulational instability (MI) of plane waves under competing nonlocal cubic-local quintic nonlinearities. The generic properties of the MI gain spectra are then demonstrated for the Gaussian response function, exponential response function, and rectangular response function. Special attention is paid to competing nonlocal cubic-local quintic nonlinearities on the MI. We observe that the focusing local quintic nonlinearity increases the growth rate and bandwidth of instability contrary to the small values of defocusing local quintic nonlinearity which decrease the growth rate and bandwidth of instability. Numerical simulations of the full model equation describing the dynamics of the waves are been carried out and leads to the development of pulse trains, depending upon the sign the quintic nonlinearity.     

On the surface waves in an elastic micropolar and microstretch medium with nonlocal cohesion

Summary A brief review of the main points of Eringen's theory of micromorphic bodies is first given, and balance equations for the linear isotropic micropolar and microstretch body are established. By appeal to the Fourier exponential transformation, nonlocal constitutive equations are derived, and assumptions with regard to the nonlocal moduli are made. The general field equations governing the propagation of a nonlocal surface wave are particularized so as to coincide with the results obtained directly in references [12], [17], [22], and [23], respectively. As an illustrative example, propagation of a microrotation and microstretch wave in a nonlocal medium in the entire Brillouin zone is examined.     

New X-wave solutions of free-space scalar wave equation and their finite size realization

Based on the method proposed by Donnelly and Ziolkowski [1], [2], a new general solution has been obtained for the isotropic/homogeneous scalar wave equation in cylindrical coordinates. It is shown that well-known limited diffraction beams such as Durnin's Bessel beams [4], Lu and Greenleaf's X-wave [15], localized waves of Donnelly and Ziolkowski [1], [2], and limited-diffraction, band-limited waves of Li and Bharath [19], [20] can be obtained from this generic solution as particular cases. In addition, we have obtained new X-wave solutions and have calculated the field characteristics for one of them using a finite aperture realization. It is shown that with a proper choice of the free parameter values, well-behaved X-waves with narrow beamwidths and large depths of field can be achieved. For similar source spectra, the results are compared with Lu and Greenleaf's zeroth-order X-wave, and it is shown that the depth of field and beamwidth are very comparable.     

On the nonlocal effects in an elastic layer subject to gravity and compression

An elastic infinite layer resting on a rigid foundation and subject to the gravity force and compression is examined in the context of a linear nonlocal theory. Eringen's solution of an auxiliary problem, involving plane-wave propagation in an infinite elastic space ([1]–[3]), furnishes the formula for the nonlocal moduli in their Fourier transform form. The latter, inverted and combined with the equation of equilibrium of the layer and the equation of nonlocal stress in the form of Kroener-Eringen, leads to a difference equation of the second order with $\text{N}$ constituent second differences. Its solution for the nearest atom interactions reduces to the trivial traditional solution, but differs from the latter if the interactions of more distant atoms are considered. Numerical examples involving aluminum and lead show a satisfactory agreement of the theory with experiment.     

Surface green function matching for a three-dimensional nonlocal continuum

With a view toward helping to bridge the gap, from the continuum side, between discrete and continuum models of crystalline, elastic solids, explicit results are presented for nonlocal stress tensors that describe exactly some lattice dynamical models that have been widely used in the literature for cubic lattices. The surface Green function matching (SGFM) method, which has been used successfully for a variety of surface problems, is then extended, within a continuum approach, to a nonlocal continuum that models a three-dimensional discrete lattice. The practical use of the method is demonstrated by performing a fairly complete analytical study of the vibrational surface modes of the SCC semi-infinite medium. Some results are presented for the [100] direction of the (001) surface of the SCC lattice.     

Modulational instability of electromagnetic waves in long Josephson junctions

This paper examines the modulational instability of electromagnetic waves in long Josephson junctions under conditions where the electrodynamics of the junction are nonlocal. A region is found containing a modulational instability of nonlinear plane electromagnetic waves in the junction. Pis’ma Zh. Tekh. Fiz. 23, 8–11 (January 26, 1997)